Diophantine approximations and toric deformations (Q1409319)

Some time ago the reviewer and G. Wüstholz applied the (then new) product theorem in Diophantine approximation to subvarieties of projective spaces, and obtained a new proof of Schmidt's theorem (on linear forms). The exponents in these result where governed by invariants of filtered vector-spaces. The paper under review gives a systematic treatment of these invariants for subvarieties of projective spaces, mainly in terms of their Chow-forms. At the end the author gives many examples of the results which can be achieved by this method.